Natural break-up and satellite formation regimes of surfactant-laden liquid threads. (25th January 2020) - Martínez-Calvo, A.; Rivero-Rodríguez, J.; Scheid, B.; Sevilla, A.
Abstract : Abstract : We report a numerical analysis of the unforced break-up of free cylindrical threads of viscous Newtonian liquid whose interface is coated with insoluble surfactants, focusing on the formation of satellite droplets. The initial conditions are harmonic disturbances of the cylindrical shape with a small amplitude [STIX]x1D716, and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit [STIX]x1D716→ 0, the problem depends on two dimensionless parameters, namely the Laplace number, La=[STIX]x1D70C[STIX]x1D70E_0R/[STIX]x1D707^2, and the elasticity parameter, [STIX]x1D6FD=E/[STIX]x1D70E_0, where [STIX]x1D70C, [STIX]x1D707 and [STIX]x1D70E_0 are the liquid density, viscosity and initial surface tension, respectively, E is the Gibbs elasticity and R is the unperturbed thread radius. A parametric study is presented to quantify the influence of La and [STIX]x1D6FD on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite's surface just prior to pinch-off, V_sat and [STIX]x1D6F4_sat, respectively. We identify a weak-elasticity regime, [STIX]x1D6FD0.05, in which the satellite volume and the associated mass of surfactant obey the scaling law V_sat=[STIX]x1D6F4_sat=0.0042La^1.64 for La2 . For La10, V_sat and [STIX]x1D6F4_sat reach a plateau of about 3 % and 2.9 %, respectively, V_sat being in close agreement with previous experiments of low-viscosity threads with clean interfaces. For La<7.5, we reveal the existence of a discontinuous transition in V_sat and [STIX]x1D6F4_sat at a critical elasticity, [STIX]x1D6FD_c(La), with [STIX]x1D6FD_c→ 0.98 for La0.2, such that V_sat and [STIX]x1D6F4_sat abruptly increase at [STIX]x1D6FD=[STIX]x1D6FD_c for increasing [STIX]x1D6FD . The jumps experienced by both quantities reach a plateau when La0.2, while they decrease monotonically as La increases up to La=7.5, where both become zero.